Alpha and Omega

A transcription—

"Now suppose that α  is an element of order 23 in M ₂₄ ; we number the points of Ω
as the projective line ∞, 0, 1, 2, … , 22 so that α : i → i  + 1 (modulo 23) and fixes ∞. In
fact there is a full L ₂ (23) acting on this line and preserving the octads…."

— R. T. Curtis, "A New Combinatorial Approach to M ₂₄ ,"
Mathematical Proceedings of the Cambridge Philosophical Society  (1976), 79: 25-42